Where could I find data series concerning population and immigration numbers in the Roman Empire? Is there even any information regarding this subject?
A wide variety of data is available on "The Digital Atlas of Roman and Medieval Civilization (DARMC) makes freely available on the internet the best available materials for a Geographic Information Systems (GIS) approach to mapping and spatial analysis of the Roman and medieval worlds. DARMC allows innovative spatial and temporal analyses of all aspects of the civilizations of western Eurasia in the first 1500 years of our era, as well as the generation of original maps illustrating differing aspects of ancient and medieval civilization. A work in progress with no claim to definitiveness, it has been built in less than three years by a dedicated team of Harvard undergraduates, graduate students, research scholars and one professor, with some valuable contributions from younger and more senior scholars at other institutions. For more details on who we are, please see the People page."
Alas, no population studies, except for an archaeological study of rat populations by region.
Roman Empire population statistics are very limited. Colin McEvedy and Richard Jones discuss the problems and provide their best guesses in "Atlas of World Population History", a Penguin Reference Book, 1978. They provide references to published sources.